3 Answers
3

I'll post an answer (partly because of Mari-Lou A's prompt!) as there is an important point of English usage that is involved.

Certainly, only furniture experts could reasonably be expected to object if the bit of wood was referred to as a 'desk shelf'. Using desk as a 'noun-doing-an-adjective's-job' (I'm in between terminologies on these) is quite permissible and idiomatic - it can mean 'part of', 'belonging to' - even 'somehow related to' (a desk / desks) in this sense. We won't go deep into 'things related to desk-related things' like desk officer!
However, a decent dictionary will list accepted compounds such as

desk clerk

desk dictionary

desk jockey

desk officer

desk phone

desk sergeant

desk work

But I'm fairly sure 'desk shelf' will not be listed. Again, 'white van man' may well have a separate entry, but not 'purple van man'.

So, using the term 'desk shelf' here is probably as simple, clear and sensible as it gets (unless you cleverly add a highlighted picture) - but it's not an agreed and well-defined term. Without the picture, we couldn't distinguish between a one-shelf and a two-shelf desk, an above-desktop and a below-desktop shelf...

And even where 'accepted' terms are recognised by relevant authorities (Sotheby's? Miller's?) there are often international, regional, and organisational disagreements.

+1 I earnestly recommend reversion to the Classical distinction between substantive nouns and adjective nouns, which endured until 18th-century rationalizers decreed that adjectives and nouns are Different Things.
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StoneyBJun 13 '13 at 11:17

You could use desk shelf, or the shelf on my desk.
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Andrew Leach♦Jun 13 '13 at 7:46

1

Hutch (in this sense) refers to a multi-shelf top, I believe (though it might apply were the OP to include the open cabinet in the ring). The single-shelf arrangement is one I've not seen before. One often finds furniture terms that seem to be used by one particular carpenter / school, or manufacturer or antiques expert nowadays - they can be used with conflicting meanings (eg commode, girandole, buffet, court cupboard, credenza).
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Edwin AshworthJun 13 '13 at 8:38

You should write this to the OP @EdwinAshworth, it's extremely useful and pertinent answer. Mine was based on impulse until I realized my error.
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Mari-Lou AJun 13 '13 at 8:44

Doesn't the OP getting notified automatically of all comments on their question & answers?
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TrevorDJun 13 '13 at 10:20

I am an interior designer and would refer to this as a gallery shelf. This would be in the context that we are referring to a piece of furniture. There is a plethora of vocabulary to describe furniture, particularly antiques, which if not being taken in context would not guarantee a good result on google (unless a retailer had optimised that term).